Archimedes' Principle

Physics 201 Section 401
ARCHIMEDES’ PRINCIPLE
Jordan Nix
Partners: Kelsey Carter and Taylor Pfau
Date Performed: November 10, 2014
TA: Andrew Whitley

Abstract

Table 1 | Mass (g) | Mass Submerged (g) | Mass Apparent (m') (g) | Radius (cm) | Length (cm) | Length Submerged (cm) | Volume (cm3) | Aluminum | 58.50 | | 42.00 | 0.95 | 7.60 | | 21.32 | Wood | 30.50 | 8.85 | 20.00 | 1.15 | 9.89 | 2.90 | 12.05 |

Table 2 | Theoretical Density(theo) (g/cm3) | Experimental Density(exp) (g/cm3) | Percent Difference(%) | Aluminum | 2.74 | 3.54 | 29.20 | Wood | 2.54 | 2.90 | 14.17 |

Discussion In the first part, a 58.5 g aluminum cylinder was hung from a string attached to a scale and submerged in a graduated cylinder filled with water. The cylinder displaced approximately 17 mLs of water and had an “apparent mass” of 42 g while submerged. Two oppositional forces acted upon the cylinder: gravity drew it downward while buoyant force pushed it towards the water’s surface. Using Archimedes’ Principle that force on a body in a fluid is equal in magnitude to the weight displaced by the fluid, we were able to calculate the experimental density of the aluminum cylinder as 3.54 g/cm3. Measurements of the radius and length of the cylinder provided its volume and theoretical density of 2.74 g/cm^3 which confirmed Archimedes’ Principle. The principle was further confirmed by calculating a 2.99% difference between the buoyant force and the weight of the aluminum cylinder. In the second part, a 30.5 g wooden cylinder was hung from a string and attached to a scale and lowered into the water-filled graduated cylinder as much as could be submerged with the string remaining taut. The wood displaced approximately 12 mLs of water and had an “apparent mass” of 20 g while